Write an equation for the path of each of the following elliptical orbits. Then use a graphing utility to graph the two ellipses in the same viewing rectangle. Can you see why early astronomers had difficulty detecting that these orbits are ellipses rather than circles?

• Earth’s orbit: Length of major axis: 186 million miles Length of minor axis: 185.8 million miles
• Mars’s orbit: Length of major axis: 283.5 million miles Length of minor axis: 278.5 million miles